PLT OF BE99 TAXIING AT NIGHT TURNS ON WHAT HE BELIEVES IS THE TXWY AND RUNS OFF THE END OF THE RWY INTO GRASS. FOG ON WINDSCREEN AND BRIGHT LIGHTS FROM ACFT ON TXWY HAMPER VISION.

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IT WAS A DARK AND STORMY NIGHT. I REQUESTED TAXI FROM GND CTL. BOEING GND ADVISED ME TO 'TAXI N ON RWY 13L VIA TXWY A4 THEN EXIT AT TXWY A2; HOLD SHORT OF RWY 13R AT TXWY A1.' I STARTED MY TAXI THEN TURNED DOWN THE COCKPIT LIGHTING AS LOW AS POSSIBLE; TURNED ON THE DEFROST FAN AND ACTIVATED THE WINDSHIELD ANTI-ICE. THE FORWARD VISIBILITY WAS LOW BECAUSE THE WINDSHIELD WAS STILL FOGGY IN SPOTS BUT MOSTLY CLR. THE VISIBILITY OUT THE SIDES WAS ALMOST NIL BECAUSE THEY WERE FOGGED UP TOO. TAXIING N ON RWY 13L THE B757 THAT HAD PUSHED BACK; THUS BLOCKING TXWY A; TURNED ON WHAT SEEMED LIKE ALL OF HIS LIGHTS. IT MADE IT EVEN MORE DIFFICULT TO SEE BECAUSE OF THE FOG ON THE WINDSCREEN REFRACTING THE LIGHT. I DID NOT NOTICE TXWY A3 GO BY. AS I APCHED TXWY A2 I THOUGHT IT WAS TXWY A3. I STOPPED THE PLANE AND LOOKED AT MY ARPT DIAGRAM. I THOUGHT IT WAS TXWY A3 OFF MY R WING BECAUSE I COULD SEE THE TXWY A2 TXWY SIGN ABOUT 100 FT AHEAD. I ADDED PWR TO TAXI DOWN TO WHERE I THOUGHT THE TURN-OFF WAS AND ENDED UP TAXIING OFF THE END OF THE RWY INTO THE GRASS. BECAUSE OF THE HVY RAIN IT WAS QUITE SOFT AND THE ACFT STOPPED IMMEDIATELY. I SHUT DOWN THE ENGS AND CALLED FOR ASSISTANCE.